Ultrafast electron microscopy for probing magnetic dynamics

The spatial features of ultrafast changes in magnetic textures carry detailed information on microscopic couplings and energy transport mechanisms. Electrons excel in imaging such picosecond or shorter processes at nanometer length scales. We review the range of physical interactions that produce ultrafast magnetic contrast with electrons, and specifically highlight the recent emergence of ultrafast Lorentz transmission electron microscopy. From the fundamental processes involved in demagnetization at extremely short timescales to skyrmion-based devices, we show that ultrafast electron imaging will be a vital tool in solving pressing problems in magnetism and magnetic materials where nanoscale inhomogeneity, microscopic field measurement, non-equilibrium behavior or dynamics are involved.


Introduction
Magnetic materials underlie a wide range of technologies, from data storage 1 and power generation 2 to charged particle optics; 3 in fundamental science, magnetism results from spin or orbital correlations in materials, and is often linked to other ordering phenomena 4 such as superconductivity, 5 ferroelectricity, 6 and charge density waves. 7 Understanding magnetism is crucial for both development of new technological applications and disentangling couplings in strongly correlated materials. Both static and dynamic properties govern the functionality of magnetic materials; this functionality typically relies on a rapid switching or transport of the spin state. Though challenging, a wealth of insight is possible through the direct observation of light-or current-driven magnetization dynamics.
For example, tracking angular momentum flow [8][9][10][11][12] in ultrafast demagnetization is crucial for both understanding the process and for speeding it up; demagnetization at interfaces 13 may show interesting spatiotemporal dynamics. 14 Memory devices based on skyrmions-topologically stable, localized quasiparticles-involve movement of nanometer-scale magnetic textures on ultrafast timescales. [15][16][17][18][19][20][21] As ever-smaller skyrmions are produced, [22][23][24][25][26][27][28][29][30] it will be increasingly necessary to image their dynamic behavior. It may be possible to better understand the atomic-scale motion of spin and charge involved in coherent ultrafast magnetism. 31-33 Highly nonuniform dynamics could be induced by a localized change in magnetic properties, such as a laser-driven transient modification of magnetic anisotropy. 34 These examples illustrate that understanding transient magnetic properties in space and time necessitates high-temporal-resolution imaging. Several probes of magnetism have been developed for this purpose.
Photons-in the visible, 35,36 extreme ultraviolet, 37,38 or x-ray 39-41 spectral range-have been employed to image magnetic dynamics for many years. Magnetization-dependent differences in absorption or reflectivity produce image contrast, and when the timing is varied between pulses of photons used for excitation, called the pump, and pulses used for imaging, called the probe, high temporal resolution is possible. 42 Ultrashort optical pulses can initiate sudden modifications on the magnetic order (see Figure 1), such as demagnetization, 36 domain dilation, [43][44][45] and ferromagnetic-to-paramagnetic phase transitions, 46 all observed using optical pump-probe techniques. These sudden changes can result in magnon generation, 47 all-optical magnetic switching, 48 and spin currents, 49 and can be applied toward technological applications such as terahertz emitters. 50 However, ultrafast photon-based nanoscale imaging has resolution limits. For example, spatial resolution in magnetooptical Kerr effect (MOKE) microscopy is typically restricted to the micrometer scale without the aid of a near-field probe. 51 X-ray magnetic dichroism (XMCD), responsible for many discoveries of nanoscale magnetic dynamics, 15,43,[52][53][54][55][56][57][58][59] can achieve a spatial resolution on the order of ten nanometers, employing imaging beamlines either at synchrotrons with X-ray pulses of tens of picoseconds or longer, 60 or with femtosecond resolution at free-electron lasers 14 and using highharmonic sources. 61 In contrast, XMCD photoemission electron microscopy takes advantage of the spatial resolution of electron imaging. 54,[62][63][64][65] Electrons are a powerful alternative probe of magnetism on the nanoscale. Magnetic image contrast using electrons arises through both inelastic and elastic scattering. With low incident electron energy, scanning electron microscopy with polarization analysis (SEMPA) [66][67][68][69][70][71] probes the local surface magnetization by sampling the spin polarization of emitted secondary electrons, and spin-polarized low-energy electron microscopy (SPLEEM) offers magnetic contrast in reflection, 72,73 because the inelastic and elastic electron mean free paths depend on the relative orientation of electron spin and local surface magnetization. Higher incident-energy electrons can excite atomic transitions sensitive to material electron spin polarization, analogous to XMCD; this technique, called electron magnetic chiral dichroism (EMCD), employs crystalline diffraction to select outgoing electron orbital angular momentum states corresponding to different transitions. 74 EMCD offers atomic-resolution magnetic contrast, 75-77 but the high dose necessary for a good signal-to-noise ratio may restrict the usability of this technique for short electron pulses. Magnetic dichroism with electron orbital angular momentum post-selection 78-82 relies on similar mechanisms but has the potential for an adequate signal-to-noise ratio even with femtosecond pulses and kHz repetition rates. Spin-polarized transmission electron microscopy 83,84 may prove capable of both inelastic and elastic magnetic imaging.

Lorentz transmission electron microscopy
The Lorentz force, an elastic interaction, can be employed for magnetic imaging at a wide range of energies. 85 Lorentz electron microscopy describes modes where the immersive objective lens of a transmission electron microscope is turned off to minimize the external magnetic field applied to a magnetic specimen, and imaging contrast is based on the Lorentz force, as shown in Figure 2. Three contrast modes are most commonly used for magnetic imaging in transmission electron microscopy: (1) Fresnel contrast, 86,87 which uses image defocus to transform phase gradients introduced by the Lorentz force onto incident plane wave-like electrons into intensity in an image (Figure 2b and d); (2) differential phase contrast, 88 which uses a focused beam at the specimen and measures the deflection in momentum space due to the Lorentz force with a quadrant or pixelated detector (Figure 2c and e); and (3) holography, 89,90 which uses a biprism to interfere the plane wave passed through the specimen with an off-axis reference wave passed through vacuum. Fresnel contrast is most frequently used for its simplicity, whereas differential phase contrast is more quantitative and increasingly applied as fast pixelated detectors become more common. Holography is the most quantitative of the three contrast modes, but also requires a high transverse coherence, 91 so it is challenging but possible with pulsed electrons. 92,93 With a pulsed electron source 94 through either photoemission 92,95-100 or a beam chopper, [100][101][102][103][104][105] and synchronized current, field, or laser excitation of the specimen, sub-picosecond temporal resolution has become possible in stroboscopic transmission electron microscopy. [106][107][108] This approach has many applications, but some of the first experiments imaged magnetic dynamics with Lorentz microscopy. 101,109 Moreover, using continuous-beam imaging and in situ short-pulsed excitation of a sample, insights into the ultrafast generation and stabilization of quenched magnetic states are possible. [110][111][112][113][114]

Imaging optical pulse-induced magnetic textures
Standard Lorentz microscopy is an excellent tool to investigate magnetic textures induced by femtosecond optical excitation. Imaging the response of magnetic textures to external stimuli has a long tradition. Commonly, variations in temperature 115,116 and temperature gradients, 117  magnetic fields [118][119][120] or electric currents 121,122 are applied on timescales for which the spin system remains close to local thermal equilibrium. In contrast, in situ femtosecond optical excitation results in a far-from-equilibrium spin state and enables the creation of novel metastable magnetic textures, which can be characterized by continuous-beam Lorentz microscopy, as shown in Figure 3.
As a first example, Eggebrecht et al. recently demonstrated the optically induced generation of a dense vortex-antivortex network in a polycrystalline iron thin film deposited on a silicon nitride membrane. 112 Before excitation, the system shows a magnetic ripple texture, induced by the local fluctuations of the magnetic anisotropy direction (see Figure 3a, upper panel). Applying a single intense ultrashort optical pulse raises the temperature of the iron thin film above the Curie temperature. In the center of the optical focal spot, the iron thin film is transiently demagnetized, whereas the underlying silicon nitride membrane remains cold. On a 100 ps timescale, the iron film thermally equilibrates with the membrane and a local ferromagnetic ordering is re-established, but the fast cooling rate (larger than 10 12 K/s) prevents the system from reaching a homogeneous ordering. Instead, nanoscale ferromagnetic domains are formed, which, at their mutual boundaries, are linked by topological vortex and anti-vortex defects. The "frozen" magnetic state, as shown in Figure 3a (lower panel), is stable at room temperature but can be reset to the initial ripple texture by either applying an external magnetic field or lowfluence optical pulses.
Similar results were obtained for optically excited permalloy (Ni 80 Fe 20 high permeability magnetic alloy) microstructures, in which vortex switching and smallscale vortex-antivortex networks can be induced. 113 In this case, the probability of the final magnetic configuration was shown to depend on the strength of the optical excitation and the shape and size of the magnetic structure.
While out-of-plane magnetized samples are generally less suited for Lorentz microscopy, local topological defects such as domain walls or skyrmions can still provide good image contrast with nanoscale resolution. 119 In a recent study, 114 the optical generation of a metastable skyrmion texture in FeGe thin films was probed by in situ Lorentz microscopy. In equilibrium, FeGe shows a series of different magnetic phases depending on sample temperature and applied magnetic field. A Lorentz micrograph of a mixed phase with helical and conical textures stable at low temperatures and intermediate external magnetic fields is shown in Figure 3b (upper panel). Upon laser excitation starting from this phase, the sample temperature rapidly increases, reaching the stability regime of an adjacent skyrmion phase. Fast quenching results in a metastable skyrmion lattice, as shown in Figure 3b (lower panel). Such all-optical writing approaches could be a fundamental ingredient for novel skyrmion-based information storage and transport applications. The dynamical evolution upon femtosecond optical excitation in a related sample system was further elucidated using time-resolved x-ray scattering, demonstrating ultrafast switching and the existence of a transient topological fluctuation state. 123

Ultrafast Lorentz transmission electron microscopy
With stroboscopic electron illumination, ultrafast Lorentz transmission electron microscopy can be applied to image transient changes in magnetic textures and fast dynamics. for spatiotemporal reversibility of the triggered magnetic dynamics, often necessitating a tailored sample design.
Ultrafast Lorentz microscopy has been employed to study several types of dynamics, including domain wall motion under an oscillating magnetic field 109 or laserinduced thermal gradients, 110,124 laser-induced demagnetization, 100,124-126 and current-driven vortex oscillations. 127 In two recent examples, Möller et al. investigated the response of a magnetic vortex to an applied highfrequency current. 127,128 The interplay between the current-induced force on the vortex, consisting both of Oersted-field and spintransfer torque contributions, and the confinement potential within a magnetic nanostructure results in resonant gyration dynamics of the vortex. Driving the vortex gyration by applying 101.5 MHz radiofrequency currents across a 2.1 µm permalloy square, Möller et al. were able to track the vortex position with a 2 nm precision, 127 as shown in Figure 4, and observed the frequency dependence of the response in real space. 128 Prior work had mapped the time-averaged motion using continuous-beam Lorentz microscopy. 121 The temporal resolution available in ultrafast Lorentz microscopy now captures the precise phase of the gyration, and can measure the dissipation rate and transient ring-down behavior of the oscillation after the driving current is rapidly switched off.
As a further example, several groups have recently investigated ultrafast demagnetization, shown in Figure 5. Ultrafast demagnetization was first observed through optical Kerr spectroscopy in 1996, 36 and its underlying microscopic physical mechanisms are still being debated. 31, [129][130][131][132][133] Ultrafast Lorentz microscopy has the potential to a b 1 µm 250 nm provide further experimental insights due to its very high spatial resolution.
Several recent experiments studied demagnetization behavior with ultrafast Lorentz microscopy with picosecondscale 100,124-126 temporal resolution. Rubiano da Silva et al. recently mapped the partial demagnetization of vortices in nanoscale disks of permalloy with 100 nm spatial resolution and 700 fs temporal resolution, 125 shown in Figure 5a-c. Cao et al. reported on demagnetization of permalloy with a grating pattern caused by interference in the exciting laser, resulting in a coherently precessing magnetic grating, 126 shown in Figure 5d. Zhang et al. observed a peculiar sequence of subpicosecond demagnetization, recovery over 3 ps, and decay to a paramagnetic state over 12 ps of the spiral spin texture in Mn-Ni-Ga. 100 Despite this methodical progress, ultrafast Lorentz microscopy still needs to overcome a number of experimental challenges. Since Fresnel contrast is linked to the applied imaging defocus, reaching a sufficient signal-to-noise ratio often requires rather large defoci in the 100 µm range or above, associated with a significant loss in spatial resolution. Therefore, further progress in high-coherence, high-brightness ultrafast electron sources is necessary to reach a spatial resolution on the order of few nanometers.

Conclusion and outlook
As the experiments presented here show, behavior of magnetic materials at picosecond or shorter timescales may strongly deviate from equilibrium. This far-from-equilibrium behavior is observable with Lorentz electron microscopy both via in situ excitation of ultrafast processes that lead to long-lived changes in magnetic textures, and with stroboscopic excitation and imaging of picosecond or faster dynamics. The combination of a nanometer spatial and femtosecond temporal resolution makes ultrafast electron microscopy an excellent tool for imaging magnetic dynamics. Electron microscopes can measure crystal structure, charge states, electric fields and bonding down to the atomic scale, and strain, temperature, phononic and plasmonic band structures on the nanometer scale. The capability to correlate these properties with sub-picosecond movies of magnetic dynamics will enable identification of nanoscale inhomogeneities invisible in bulk measurements, quantification of local fields used to excite dynamics, and direct measurement of coupled behavior like magnetostriction.
Specifically, this tool is wellsuited to help answer a number of open questions in magnetism related to microscopic magnetic energy landscapes, 127,128 angular momentum transfer processes, 134 ultrafast demagnetization at interfaces, skyrmion dynamics, and coherent ultrafast magnetism. The growth of other ultrafast electron techniques, including time-resolved SEMPA 67-71 and potentially SPLEEM, opens the door to complementary surface-sensitive imaging of dynamics. New manipulation techniques, such as irradiation by a high-charge pulse of electrons, 135 may grow in use. There are numerous opportunities for ultrafast electron imaging to unravel key problems in magnetism.

Acknowledgments
We appreciate helpful discussions with Felix Büttner, and thank Markus Münzenberg and Henning Ulrichs for their contributions to some of the works presented here. We thank the UTEM team for work on maintaining the microscope. We gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG-SPP-1840 "Quantum Dynamics in Tai  acknowledges support of a Lichtenberg professorship funded by the VolkswagenStiftung.

Funding
Open Access funding enabled and organized by Projekt DEAL.

Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.

Open Access
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